There is a noise from speaker combined with speaker drive unit moving towardthe the cabin when I turned off my QUAD 405. Could anyone let me know what wrong with it and which part need to be replaced? Thanks!

Like pfiuuuuu....and than thump...and woofer cone movements....
Check Bernd Ludwig's text ....google it.
It is because op amp shuts down before rest of the amp....
You can modify a lot....add a lot ....or just leave as is. It is nothing wrong with your amp it is just old Quad.
Cheers, Taj

My experience of a Quad 405 Mk 1 clone was good, without any unpleasantness at power up or down. However, when I played about with replacing the LM318 op amp with something more modern, I got thumps at power up and, I think, even a squeal of oscillation at power down.

I just replaced op amp with OPA134 combined with two 100n wima caps for decoupling. Now the power off noise is decreased to a slight "Ssssss" and followed by a shorter con movement. Is this normal for all 405 amps?